Advanced Placement (AP), 11.12.2020 05:30 joeykyle05

Does anyone know the answer to this ?!

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Answer from: annyarias3563

Yes.

The perimeter is about 42.86 m Round to 42.9 m

The area is about 138.59 m² . Round to 138.6 m²

Explanation:

To find the perimeter, you need the length of the sides. Imagine the octagon as 8 isosceles triangles assembled. You need the length of the short (exterior) side to calculate the perimeter.

With only the length of the ray given, you could use some trig. A calculator is necessary!

The octagon has 8 sides, you can calculate the size of the central angle between two radii 360/8 = 45. Subtract from 180 and divide by 2 to get the measure of one of the equal angles.

That angle measure is 67.5° Use cos(67.5)(7) = 2.678784027 the length of half of the side-- between the dotted line and the ray in the diagram.

2(2.678784027)(8) = 42.86054443 is the perimeter.

The area of each isosceles triangle is bh/2.

Find the height by using sin(67.5)(7) = 6.467156728

The cos(67.5)(7) is already half the base. Use as is!

6.467156728 × 2.678784027 = 17.32411614

This is the area of 1 of the 8 imaginary triangles, so multiply by 8 for the whole area of the octagon.

17.32411614 × 8 = 138.5929291

I hope this helps. Complicated!

There may be easier ways, but this is the only way I know at this point.

Answer from: Quest

.: |: . answer .: |: .

being judged during everyday activities lowers your self esteem

.: |: . evidence \ reasoning .: |: .

when doing your every day activities, it feels like a normal routine. there is nothing wrong with you doing what you do every day. but what happens when you start to get judged? what happens when the things that you used to normally do are being picked apart and thought-down on? that might lower your self esteem. you might start to feel depressed or uncomfortable. you were just doing your everyday life, right? if my schedule and day to day life started getting pulled apart and judged, i would get upset, and possibly mad. i wouldn't want to do my schedule everyday, knowing that it was going to get judged. being picked and judged would affect your life because not only is someone else thinking down on you, you start to think down on your life. you start to feel that your worth lowers, and that your worth is in the hands of someone else.

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Answer from: Quest

You need to figure out at which x-value does the graph has a tangent line slope of -1.remember, the derivative is the slope of the tangent line. so find the derivative function and set it to equal -1 to find the x-value that will have a tangent line slope of 0.differentiate with the chain rule. $\begin{aligned} f(x) & = (0.5)^{2x} \\ f'(x) & = 0.5^{2x} \cdot \ln(0.5) \cdot (2x)' \\ f'(x) & = 0.5^{2x} \cdot \ln(0.5) \cdot 2 \\ f'(x) & = 2\ln(0.5) \cdot 0.5^{2x} \end{aligned}$ set the derivative to equal -1 and solve for x. $\begin{aligned} -1 & = 2\ln(0.5) \cdot 0.5^{2x} \\ -\frac{1}{2} & = \ln(0.5) \cdot 0.5^{2x} \\ -\frac{1}{2\ln(0.5)} & = 0.5^{2x} \end{aligned}$ take log base 10 of both sides. also recall that $\log_c(m^n) = n \log_c m$ . $\begin{aligned} \log\left[ -\frac{1}{2\ln(0.5)}\right] & = \log\left[0.5^{2x}\right] \\ \log\left[ -\frac{1}{2\ln(0.5)}\right] & = 2x \log(0.5) \\ \dfrac{\log\left[ -\frac{1}{2\ln(0.5)}\right]}{2\log(0.5)} & = x \\ x & \approx 0.2356 \end{aligned}$ so the x-coord of the point of tangency is $x \approx 0.2356$ .the y-coordinate of this point of tangency can be calculated using the original function: $\begin{aligned} f(x) & = (0.5)^{2x} \\ f(0.2356) & = (0.5)^{2 \cdot 0.2356} \\ & \approx 0.7213 \end{aligned}$ using point-slope form, the equation of the tangent line is $y - 0.7213 = -1(x-0.2356)$ the x-intercept of this tangent line is when the graph is at y=0. $\begin{aligned} 0 - 0.7213 & = -1(x-0.2356)\\ - 0.7213 & = -(x-0.2356) \\ 0.7213 & = x-0.2356\\ x & = 0.9569 \end{aligned}$ this rounds off to $x & = 0.957$ .choice c.

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